Supplier selection for vendor-managed inventory in healthcare using fuzzy multi-criteria decision-making approach

This paper purposes a comprehensive multi-criteria decision making (MCDM) to select the best potential supplier for VMI collaboration in healthcare organization.

* Corresponding author

E-mail address: dettoy999@gmail.com (D Sumrit)

© 2020 by the authors; licensee Growing Science, Canada

doi: 10.5267/j.dsl.2019.10.002

Decision Science Letters 9 (2020) 233–256

Contents lists available at GrowingScience

Decision Science Letters

a local famous public hospital and the best potential supplier was selected The study reveals that the most evaluation criteria when selecting supplier for VMI in healthcare sector are institutional trust, information sharing and exchanging as well as information technology

Vendor managed inventory

Multi-criteria decision making

an initiative and collaborative tool that allows suppliers authorized to manage inventory of customers (Kros et al., 2019) A great deal of evidences from previous studies have presented that VMI provides many benefits to various industries Savasaneril and Erkip ( 2010) indicated that VMI can generally offers benefits to both suppliers and customers via their agreement frameworks in order to ensure

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product availability for customers and to provide flexibility to suppliers In the same way, the study of Yao et al (2007) also defined that there are higher potential economic benefits after adopting VMI such as inventory cost reduction for the suppliers, and service level improvement for customers, i e , higher repeated rate

Several empirical researches have broadly conducted VMI usages, applications, and enablers, which are in various business in manufacturing sectors like automotive, electronics, telecommunication, retail industries and even hospital (Dong & Xu, 2002) For example, the optimal pricing and lot sizing vendor managed inventory (Ziaee & Bouquard, 2010), a comparison of performance results of VMI practices and define enablers of successful VMI usages (Classen, et al., 2008) Some literatures have discussed VMI in various useful aspects of manufacturing sectors; for example, production- distribution planning/ supply chain management ( Niknamfar, 2015) , home appliances industry ( Tony & Zamalo, 2005) , inventory and pricing policies in non- cooperative supply chain ( Naeij & Shavandi, 2010) Regarding to VMI advantages, it is increasingly used in many industries for day- to- day operations of several organizations The successful VMI implementation can contribute numerous benefits to improve supply chain performance of hospitals, i.e., the improvement of efficiency, responsiveness, and replenishment process; the reduction of unnecessary overstocks or stocks out situations; including decreasing uncertainty for production and operational planning and so on (Volland et al , 2017) As pinpointed by Kim (2005), VMI implementation program of hospitals can lead 30% of stock reduction

in medical and pharmaceutical products Moreover, there might be some barriers of VMI practices in healthcare sector such as lacking of knowledge and skills in supply chain management, i.e., technology involvement, standardize code, physician preference, information sharing limitation and poor supplier selection (Guimarães et al., 2013) Krichanchai and MacCarthy (2017) stressed that suppliers play an important role in achieving VMI project initiative The supplier selection should be careful since it is one of the crucial organizational decisions for VMI implementation and greatly depend on suppliers (Classen et al , 2008) Bhakoo et al (2012) found that a poor supplier selection decision- making consequently brought the negative impact of VMI performance

There is an increasing trend to adopt outsourcing inventory decision to suppliers in healthcare sector because many hospitals pursue to improve inventory costs and service levels to deliver their services

in time manner ( Kwon et al , 2016) Hence, the appropriated supplier selection in VMI program is significantly crucial to reach the success of healthcare organization which relies on the supplier’ s capabilities and performances Even though there have been numerous bodies of knowledge from literature related to supplier selection, there are still the limited studies on supplier selection toward initiative VMI From the extensive literature, this paper is deemed as the first pioneer in VMI supplier selection in context of healthcare sector Thus, this research attempts to fill a gap within the body of knowledge by proposing a comprehensive framework for selecting VMI supplier To obtain aforementioned above, this study has five following objectives especially in healthcare context: (i) to propose a comprehensive fuzzy decision making framework for VMI supplier selection in healthcare context, ( ii) to identify evaluation criteria for VMI supplier selection, (iii) to determine the relative importance weights of the VMI supplier selection criteria, (iv) to select the potential supplier for VMI implementation by using a famous public hospital in Thailand as a case study, and (v) to address managerial and practical implications

This paper provides three genuine contributions as follows Firstly, the study conducted extensive literature to develop a set of evaluation criteria, which specifically uses for VMI supplier selection Secondly, this study proposed comprehensive Fuzzy MCDM framework for VMI supplier selection by taking vagueness and uncertain human decision making into consideration Finally, the proposed framework was applied to select the best VMI supplier by using one of the famous public hospitals in Thailand as a case study

The rest of the paper is organized as follows: it starts with an overview of VMI literature and the fields

of VMI in healthcare sector and methodology theoretical theories supporting for this research Then it

discusses the proposed research framework and problem descriptions before transitioning to results Last section includes conclusions, implications, and directions for future research

2.1 VMI in Healthcare Industry

Traditionally, owners or managers in healthcare industry has paid less attention to supply chain management, especially to inventory management Actually, this concern has significantly been recognized due to pressures of inventory cost and huge physical & information flow of medical and pharmaceutical products (Guimarães et al , 2013) The VMI implementation in hospital is considered

as one of the most effective integrated tools for both suppliers and hospitals Its purposes are to (i) reduce inventory levels & transportation costs, (ii) improve levels of resources supply, speed, and product availability, ( iii) increase customer service levels and ( iv) reach a higher accuracy of forecasting and demand planning ( Kim 2005) Healthcare products normally divide to medicine and pharmaceutical supplies It is highly potential to adopt VMI for the pharmaceutical products because the pharmaceutical suppliers have knowledge on material management, acquaintance with information technologies (IT) and supply chain management with the best practices (Kim, 2005) In addition, pharmaceutical sector has been strategically implementing IT solutions from entire logistics processes

as cross-docking to VMI, streamlining the replenishment process (Shih et al., 2009)

VMI in healthcare industry can create the effective supply for both healthcare organizations and suppliers to reduce the inventory cost Simultaneously, it is very useful for hospital warehouse management to improve inventory levels & product availability, develop accuracy & speed of resources

or supply, and reach the most effective distribution of resources ( Hui, 2010) Healthcare industry operations are mainly to manage costs for purchasing inventory in the appropriated amounts without overstocking By VMI implementation, suppliers can assist healthcare organization to identify the replenishment of stocks based on frequency, volume and time Also they can reach ordering flexibility, reduce lead time variability & transportation costs, optimize physical distribution, increase warehouse efficiency, access to real time information, and enhance competitive advantage relations (Sui, 2010) Despite several benefits, there might be potential risks related to VMI implementation; for example, shortage of trust and reliability among supplier partners, high investment cost, especially in IT infrastructure in order to accommodate information sharing and time consuming Other problems on VMI implementation also cover long purchase ordering process, less electronic process, lack of controlling power and forecast sales of suppliers (Ngampunvetchakul, 2014) Also there might be some barriers of VMI practices in healthcare sector; such as lacking of knowledge and skills in supply chain management, i.e., technology involvement, standardize code, physician preference, information sharing limitation and poor supplier selection (Guimarães et al , 2013) Nevertheless, only few prior researches have studied in healthcare sector (Matopoulos & Michailidou, 2013)

There are several previous studies analyzing total costs of supply chain from VMI adaption; notwithstanding there are some problems on making a decision on inventory levels or supply chain cost without sharing information at point of sale Then such VMI models could not be well performed since vendor could not access the real demands of products and unable to forecast inventory level Few research studied VMI implementation be successful in hospital, e.g., Dong and Xu (2002) represented VMI benefits to be useful to reduce stock holding; Classen, et al (2008) suggested supplier relationship with good IT infrastructure resulted from VMI usage; Hui (2010) suggested supply chain management

in hospital based on VMI; and Bhakoo et al ( 2012) found that various benefits were perceived from collaborative agreements among supply chain of hospital partners Moreover, healthcare sector, as a part of service industry, has been extensively studied in several aspects; for example, an influence of the related parties through inventory systems in healthcare (De Vries, 2011) , a making decision on an appropriated product selection for professional healthcare staffs ( Chen et al , 2013) , an explore of the impact of VMI practices on warehouse and inventory management of hospital (Ngampunvetchakul,

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2014); cost-benefit sharing in healthcare supply chain collaboration (Niemsakul et al., 2018); a criteria decision making model for readiness assessment of vendor managed inventory in healthcare (Sumrit, 2019); and a generic framework for hospital supply chain (Ziat et al., 2019)

multi-2.2 VMI Supplier selection criteria

One of the essential procedures in Multi- Criteria Decision Making (MCDM) approach is the determination of the proper criteria Since, from many previous studies, the criteria of VMI supplier selection in healthcare sector are rarely addressed Hence, this study focuses on the extracted criteria from VMI both in healthcare and related neighbor service industries The lists of applicable of such criteria is carefully developed as displayed in Table 1

Table 1

Lists of criteria used for the VMI supplier selection

Past delivery

performance

Refers to the ability of the pharmaceutical supplier consistently supplies the acceptable healthcare products to hospital warehouse at the predefined delivery schedule Such performances include the abilities to manage lead time, on time, location and fill rate The well performed supplier in delivery performance should have a potential to engage VMI in hospital (Krichanchai & MacCarthy (2017)

Institutional trust Defines as pharmaceutical suppliers honestly show their trust, and real motivations, goals, and agendas for VMI process

Abdallah et al., ( 2017) affirmed that the suppliers need to develop trust and a relationship with their healthcare providers to

c o l l a b o r a t e a n d s h a r e i n f o r m a t i o n p e r t a i n e d t o d e m a n d a n d i n v e n t o r y l e v e l s

Investment cost Refered to VMI total investment cost of the initiative project implementation of both hospital and pharmaceutical supplier

VMI implementation may create cost burden because it is certainly required investment and restructuring costs, which would consume both parties’ working capitals (Dong et al., 2007)

Information sharing

and exchanging Refers to process which a hospital and a pharmaceutical supplier timely and jointly share and exchange a range of relevant and accurate information Raweewan and Ferrell ( 2018) mentioned that information sharing between healthcare provider

and medical suppliers can lead to reduce uncertainty in inventory management collaboration Ramanathan ( 2012) also confirmed that information sharing would support the supply chain partners to collaborate in inventory polling and joint replenishments

Continuous

improvement

Defines as the ability of a pharmaceutical vendor to consistently conduct of continuous improvement activities in VMI process Kwon et al., (2016) presented that a lack of suppliers’ capability and skills in performing continuous improvement caused a healthcare provider unwilling to adopt VMI

Supply chain process

integration

Refers to the hospital and the pharmaceutical supplier integrate the relevant supply chain processes incorporation with VMI management Shou et al., (2018) stressed that supply chain integration can enhance information-sharing mechanisms between both parties Also, Flynn et al., (2016) defined the establishment of supply chain integration process is essential for VMI project initiative

Information

technologies readiness

Refers to enabling information technology used in managing supply chain operation by the pharmaceutical supplier The VMI implementation needs to handle the complicated flow both information and physical stocks for dealing with demand uncertainty (Kros et al., 2019) Supplier still requires sophisticated information technology system to manage such complex operation (Moons et al., 2019)

Supplier flexibility Refers to the ability of the pharmaceutical supplier to respond the changing of hospital’s demand and requirements Jayaram

et al , (2011) noted that supplier’ s flexibility could influence VMI adoption for many organizations Supplier flexibility facilitates the positive impact of the relational buyer-supplier strength (Yang et al., 2019)

Project

implementation time

Refers to length of time to complete VMI initiative project implementation between a pharmaceutical vendor and the hospital, Dong et al., (2007) examined that healthcare provider tends to resist VMI adoption if project spends much time length

Devoted resources Refers to a commitment resources from a pharmaceutical vendor to setup and implement VMI system The VMI system

implementation might require the use of robust information technologies such as electronic data interchange (EDI) and data tracking devices, which are considerably expensive to establish and maintain (Vigtil, 2007) Hence, lack of supplier’ devoted resources is one of the obstacles for VMI project initiative (Dong et al., 2007)

Spatial complexity Refers to the geographic distance between the pharmaceutical supplier warehouse and hospital in order to execute

replenishment in VMI process The literature highlighted that the considerable geographical distance between the healthcare provider and the pharmaceutical vendor is negatively affected to VMI feasibility because risks in supply chain disruption would possibly lead to severe consequences for healthcare service (Danese, 2007)

Prior knowledge and

experience

Defines as the level of technological knowledge and experience of pharmaceutical supplier in handling similar VMI project Vigtil (2007) observed that the supplier’ prior experience in VMI project can lead to greater advantages such as cost saving, quality improvement, mitigate risk in inventory collaboration processes

Risk/ Reward Sharing Define as the agreement between the pharmaceutical supplier and hospital in sharing of costs, risks, and benefits for VMI

processes Uncertainties in demand and pricing of healthcare products result in a situation where the pharmaceutical supplier and the hospital supplier encountering the risk of shortages, delays and financial losses (Danese, 2007)

Reputation and

position in industry

Define as the ranking and reputation of the pharmaceutical supplier compared with its competitors in the same industry in term of brands, products and firms image According to Watt et al., (2010), supplier reputation is recognized as an important criterion in overall evaluation of company

2.3 MCDM Methodology

2.3.1 Fuzzy set theory

In 1965, Fuzzy set theory was introduced by Zadeh (1965) to deal with problems involving uncertainty, vagueness, and the utilization of linguistic terms to describe the decision maker’ s choices Linguistic terms are utilized to represent variables, which are associated with fuzzy sets and membership function Linguistic terms are expressed by natural sentences and converted into triangular fuzzy numbers (TFNs) TFNs were practically applied to handle the vagueness of the linguistic assessments and to contribute the easy usage and computation (Kannan et al., 2014) Many research have applied fuzzy theory in various context; for example, Raad N.G et al., (2019) used fuzzy MCDM to select a portfolio

of projects considering both optimization and balance of sub-portfolios Abbady et al (2019) applied fuzzy sets approach for big data governance, dynamic capability and decision-making effectivenes Chatterjee and Bose (2013) employed fuzzy MCDM for selection of vendors for wind farm In this study, linguistic terms from Table 2 is used to calculate the relative importance weight of criteria and

Table 3 is displayed the rating scale for alternatives TFNs can be formed by using a triplet ( l, m, u) where the membership function of the fuzzy number F(x) is defined in Fig 1 and expressed as in Eq

l

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2.3.2 Linguistic variable

A linguistic variable is a variable that is expressed in linguistic terms such as artificial words or natural

sentences which are then displayed by triangular fuzzy numbers (Kannan et al , 2014) This study

adopted linguistic scale from Table 2 to derive the relative importance weight of criteria And Table 3

shows the linguistic scale to evaluate the ratings of alternatives

Table 2

The fuzzy scale for the relative weight of criteria (Chang, 1996)

Table 3

Linguistic scale to evaluate the ratings of alternatives (Chang, 1996)

The Fuzzy Delphi method is an integration of fuzzy set theory and traditional Delphi method ( Lee et

al , 2010) Fuzzy Delphi has major advantages such as reducing the number of rounds in required

survey; appropriately dealing with vagueness, ambiguity and uncertainty in experts’ judgment decision

process; and gaining economic and effectiveness in term of time and cost in surveys process This study

applied Fuzzy Delphi method by using the paired TFNs in a scale from 1 to 10 (Wei & Chang, 2008)

The stage of Fuzzy Delphi method is presented as follows (Wang, 2015):

Step 1: Organize the Fuzzy Delphi-based questionnaire to gather data from a group of experts By using

score value ranging from 1 to 10, each expert provides his or her score values for both most pessimistic

(minimum) and most optimistic (maximum) for each criteria (i th)

Step 2: Examine data obtained from step1 and remove outlier data from each criteria ( i th) , which are

outside two standard deviations for both pessimistic and optimistic groups From the remaining of data,

the minimum (𝑃 ), geometric mean (𝑃 ), and maximum (𝑃 ) of pessimistic group for each criteria (ith)

are determined By the same way, the minimum (𝑂 ), geometric mean (𝑂 ), and maximum (𝑂 ) of

optimistic group for each criteria (i th) are obtained

Step 3: Establish TFNs of pessimistic value 𝑃 = (𝑃 , 𝑃 , 𝑃 ) and optimistic values 𝑂 = (𝑂 , 𝑂 , 𝑂 )

for each criteria (i th) as displayed in Fig 2 According to Fig 2, the overlapping area of two TFNs (𝑃

and 𝑂 ) is defined as grey zone ( Lee et al , 2010) The grey zone is used to verify the consistent of

experts’ judgment for each criteria by comparison with the consensus significance value (𝐺 ) The

greater 𝐺 is, the higher level of experts’ consensus Thus, it is implied that criteria ith is an important

criterion

Step 4: Check the consistency of experts’ judgments and compute the consensus significance value

(𝐺 ) for each criteria (ith) as three following conditions:

Condition 1: The paired TFNs between pessimistic value (𝑃 ) and optimistic values (𝑂 ) do not overlap (𝑃 𝑂 ), indicates that there is a consensus in criteria ith Hence the consensus significance value is computed by Eq (6)

Step 5: Set up the threshold value (𝜏) for selecting appropriate criteria By making comparison between consensus significance value (𝐺 ) and threshold value ( 𝜏 ) , the evaluation criteria that consensus

significance value is less than threshold value (𝐺 < 𝜏) will be removed from consideration, otherwise

it is accepted Based on pareto 80/ 20 rule that “ 20% of the factors account for an 80% degree of importance of all factors” , the threshold value ( 𝜏 ) is arbitrary set as 𝜏 = 8 ( Somsuk & Laosirihongthong, 2017)

2.3.4 Fuzzy SWARA

The Step-wise Weight Assessment Ratio Analysis (SWARA) approach was introduced by Ker𝑠̌ullene

et al., (2010) According to Per𝜍in (2018), SWARA is one of new decision approaches, which is applied

to derive the relative importance weights of criteria or perspective

The distinctive advantage of this approach is not necessity for making several rounds in criteria weights

of pairwise comparison; like analytic hierarchy process (AHP) or analytic network process (ANP) (Mardani et al., 2017) Hence, it is simplicity in coordinating and gathering data from group of experts SWARA has been widely adopted to solve multi- criteria decision making (MCDM) problems in various contexts, e.g., Eghbali- Zarch et al (2018) applied SWARA in pharmacological therapy selection of type II of diabetes; and Yazdani et al ( 2019) used SWARA for evaluating supply chain risk management under a circular economy context The SWARA procedure is illustrated in following steps (Ker𝑠̌ullene et al., 2010)

Step 1: Arrange the evaluating criteria in descending order based on the expected significant opinions

Step 6: Convert the fuzzy relative importance weights 𝑤 to non-fuzzy (crisp value) based on Center

of Area (COA) method by Eq (11)

2.3.5 Fuzzy COPRAS

Complex Proportional Assessment of Alternatives (COPRAS) was introduced by Zavadskas, et al (1994) to be an analytic and quantitative technique of Multiple Criteria Decision Making (MCDM) for prioritizing the alternatives This approach applies a stepwise ranking and evaluation procedure of the alternatives by comparing their significance and utility degrees COPRAS has been successfully adopted to solve the decision making problems in many fields such as sustainable third- party reverse logistics provider evaluation and selection (Zarbakhshnia et al., 2018) ; hydrogen mobility roll- up site selection (Schitea et al., 2019); severity assessment of chronic obstructive pulmonary disease (Zheng

et al., 2018), etc The ranking procedure of Fuzzy COPRAS are stepped as follows:

Step 1: Determine the fuzzy decision matrix for alternatives rating by using triangular fuzzy numbers

where m represents the number of alternatives, n represents the number of criteria and 𝑥 is the

performance rating of alternative i with respect to criteria j evaluated by decision maker k, ( k =

1,2, ,K) The fuzzy numbers (xl

ijk, xm ijk, xu ijk) stand for the rating score assign to each alternative based

on Table 3

Step 2: Obtain the fuzzy aggregated decision matrix, 𝑋; by Eqs (13)-(14)

Step 4: Use fuzzy SWARA to compute the relative significant weight of each criterion

Step 5: Gain the weighted normalized decision matrix by multiplying the fuzzy weights to normalized decision matrix, as presented in Eq (4)

Step 6: Compute maximum value and total summation of each alternative, by using Eq (18)

This research proposes a framework of potential supplier selection for VMI in healthcare by integrating three approaches of MCDM, i.e., Fuzzy Delphi, Fuzzy SWARA and Fuzzy COPRAS This framework comprises of four phases, i e , ( i) extracting the supplier evaluation criteria from extensive literature review, (ii) screening the appropriate evaluation criteria by applying Fuzzy Delphi, ( iii) determining the relative importance weights of evaluation criteria by employing Fuzzy SWARA, and (iv) ranking the potential suppliers’ performance and selecting the best one by using Fuzzy COPRAS, as illustrated

an appropriate pharmaceutical supplier to attend the program By this approach, it needs a group of decision makers (DMs) which composed of six decision makers, i.e., DM1, DM2, DM3,…, DM6, in order to participate in three questionnaires (fuzzy Delphi, fuzzy SWARA and fuzzy COPRAS) These DMs have more than four- year experiences and specific knowledge in inventory management They are also a head of warehouse, two managers from purchasing department and three pharmacists from

Phase 3: Determining the relative importance weights of evaluation criteria

Phase 2: Screening the appropriate evaluation criteria Phase 1: Extracting criteria of the supplier evaluation

Phase 4: Ranking suppliers’

 Employ Fuzzy SWARA method

Phase 4:

 Apply Fuzzy CORPRAS

Fig 3 Research framework for supplier selection on VMI in healthcare

pharmacy rooms While, there are three candidate potential pharmaceutical suppliers, supposed namely Supplier A, Supplier B, Supplier C as alternatives The qualification and information of DMs are displayed in Table A- 1 and Table A- 2 of Appendix A Based on VMI supplier selection criteria from Table 1, all DMs participate in selecting the appropriated criteria, determining relative importance weight of selected criteria and evaluating such three candidate suppliers, respectively The methodology for this research applies the Fuzzy Multi- Criteria approach in order to assist a group of DMs for selecting the best supplier for VMI project implementation

5.1 Phase I: Extracting the suppliers’ evaluation criteria

As the results from the extensive literature review were presented in section 2.2, the fourteen evaluation criteria for VMI suppliers’ evaluation were extracted as exhibited in Table 1

5.2 Phase II: Screening the appropriate evaluation criteria

After obtaining the fourteen evaluation criteria, a group of decision maker provided the score values

on both the most pessimistic value and the most optimistic value on each criteria The data were then collected pass though questionnaire Fuzzy Delphi approach as mentioned in Section 2.3.4 was applied

to screen the appropriate evaluation criteria in accordance with the proposed of this study Firstly, the average scores from all DMs were computed for the conservative and optimistic values of each criterion Any value which outside two standard deviations is removed from consideration The values

of the minimum (𝑃 ) , geometric mean ( 𝑃 ) , and maximum ( 𝑃 ) of the conservative value, and the minimum (𝑂 ), geometric mean (𝑂 ), and maximum (𝑂 ) of the optimistic value were calculated and the result depicted in Table 4 Thereafter, the values of 𝑀 and 𝑍 were calculated to verify the consistency of expert judgment Subsequently, the consensus significant value (𝐺 ) for each criteria is calculated for screening the criteria by using either Eq.(6) or Eq (7) Based on pareto 80/20 rule, the threshold value (𝜏) was set at 8.0 From Table 4, since five evaluation criteria with consensus significant value were lower than such of threshold value (𝐺 < 𝜏) , they were rejected and the remaining of nine evaluation criteria (𝐺 ≥ 𝜏) were accepted, i e , Part delivery performance, Institutional trust, Investment cost, Information sharing and exchanging, Supply chain process integration, Information technologies readiness, Supplier flexibility, Project implementation time and Risk/ Reward sharing While, two criteria in Table 4 are cost criteria, i.e., Investment cost and Project implementation time And the remaining are benefit criteria The proposed model of potential supplier selection for VMI was displayed in Fig 4

Table 4

The result of Fuzzy Delphi method

Measures Pessimistic

Value Optimistic Value Geometric Mean 𝑴 𝒊 -𝒁 𝒊 Consensus

Value Decision Type Criteria of

Past delivery performance 7 8 8 9 7.65 8.41 1.35 8.03 Accepted Benefit Institutional trust 6 8 9 10 7.45 9.31 3.55 8.38 Accepted Benefit Investment cost 6 7 8 10 6.82 9.30 4.18 8.06 Accepted Cost Information sharing and exchanging 7 8 9 10 7.82 9.65 3.18 8.74 Accepted Benefit Continuous improvement 5 7 6 8 5.62 6.80 1.38 6.37 Rejected Benefit Supply Chain Process Integration 6 8 8 9 7.63 8.49 1.37 8.06 Accepted Benefit Information technologies readiness 7 8 9 10 7.82 8.63 3.18 8.23 Accepted Benefit Supplier flexibility 6 8 8 9 7.63 8.46 1.37 8.04 Accepted Benefit Project implementation time 6 7 8 10 6.65 9.47 4.35 8.06 Accepted Cost Devoted resources 4 7 6 8 5.35 6.95 1.65 6.37 Rejected Benefit Spatial complexity 4 6 5 8 4.75 6.43 2.25 5.53 Rejected Benefit Prior knowledge and experience 5 6 6 7 5.48 6.65 1.52 6.06 Rejected Benefit Risk/Reward Sharing 7 8 8 9 7.65 8.65 1.35 8.15 Accepted Benefit Reputation and position in industry 4 6 5 7 4.93 5.77 1.07 5.42 Rejected Benefit

* Remark: Criteria with the consensus significance value ( 𝐺 ) lower than threshold value (𝜏 ) are rejected

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Fig 4 The proposed model of VMI supplier selection

5.3 Phase III: Determining the relative importance weights of evaluation

Based on Table 2, the same group of decision makers expressed their judgments to determine the relative importance weight of each criterion in linguistic term as shown in Table A- 1 of Appendix A Then, the collected data from group of DMs were converted to the correspondence TFNs Fuzzy SWARA method as described in Section 2 3 4 was employed to compute fuzzy weight for each criterionby using Eqs (8)-(10), respectively The fuzzy weight data of each criteria was transformed

to non-fuzzy by Eq (11) And the relative importance weight of each criteria was presented in Table 5 According to Table 5, Institutional trust (C1) is found to be the most important criteria with the relative weight of 0 440, followed by Information sharing and exchanging ( C2) with the relative weight of 0.230, and then Information technologies readiness (C3) with the relative weight of 0.127 While Part delivery performance (C7), Investment cost (C8) and Project implementation time (C9) were the three smallest important criteria with the relative weights of 0.023, 0.016, and 0.012, respectively

)9C(Project implementation time

)7C(Past delivery performance

)

5

C

(Supplier flexibility

)6C(reward sharing /

Risk

Information technologies readiness

)3C(

)

4

C

(Supply chain process integration

)1C(Institutional trust

Information sharing and exchanging

)2C(